Although our users' pricing and privacy models need real-world evaluation, they capture the essence of our model and permit the full development and testing of our proposed algorithms. The functioning of the algorithms is unaffected by the particular pricing and privacy models. For example, other privacy preserving frameworks, such as spatial cloaking [1]}, differential privacy [2]} or Geo-Indistinguishability [3]}, could also be used instead of the Gaussian noise. In that case, the parameters in those frameworks, e.g. \(\epsilon \)  in differential privacy, can be derived from a function \(\epsilon = f_1(q_i)\)  of the price \(q_i\)  with a similar or more complicated pricing model. The noise level \(\sigma _i\)  then can be derived from a function \(\sigma _i = f_2(\epsilon )\)  of those parameters. Eventually the noise level \(\sigma _i\)  can still be considered as a function \(\sigma _i = f(q_i) = f_1\big (f_2(q_i)\big )\)  of the price. The work on specific privacy-preserving techniques or pricing models is orthogonal to our work.
Consequently, in this presentation, we assume the privacy valuation of users and the pricing function are fixed, and we focus on the problem of the buyers maximizing their total reward (i.e. profit) with the strategy to make the final \(\textit {open}\)  or \(\textit {cancel}\)  decision described in the next section.
